Table 4.

Normalized interpolation (int) and forward dynamics (fwd. dyn.) errors for each task-constraint of the testing via-point reaching tasks.

Task	intv (×10−16)			fwd. dyn.v (×10−4)			intT (×10−16)		fwd. dyn.T (×10−4)
	Pos	Vel	Acc	Pos	Vel	Acc	Pos	Vel	Pos	Vel
13−9	4.85	6.34	3.73	1.58	17.86	0.0127	1.59	7.90	8.19	38.26
2−4	5.16	4.12	0.27	11.79	24.88	0.0201	2.50	4.02	19.53	17.86
10−5	3.43	3.66	0.66	10.90	19.31	0.0117	1.33	5.20	35.56	28.91
12−6	3.65	0.78	2.67	9.87	12.55	0.0051	3.32	2.60	5.71	11.39
3−5	2.66	2.09	0.57	3.41	1.12	0.0001	2.50	2.91	10.93	9.66
1−9	3.19	1.42	2.17	3.41	5.05	0.0011	0.88	7.14	8.94	21.68
13−7	6.38	6.13	1.78	1.33	10.89	0.0065	1.82	3.59	4.71	5.62
2−12	5.93	4.24	1.91	7.20	11.63	0.0042	2.70	5.28	22.32	13.66
10−3	2.59	3.47	0.80	11.64	24.35	0.0189	1.11	9.02	42.07	61.72
12−2	2.83	2.88	2.58	1.70	17.67	0.0099	1.77	5.78	11.47	15.36
3−8	4.42	2.24	0.48	7.42	8.21	0.0023	1.11	1.76	3.54	4.99
1−7	0.22	3.02	0.54	0.71	7.84	0.0019	2.38	3.81	15.40	6.14
13−1	6.53	6.39	2.34	2.63	20.00	0.0190	4.53	4.86	31.77	64.69
2−8	6.25	4.53	0.47	11.59	25.12	0.0203	3.07	2.69	5.25	4.44
10−11	1.89	3.20	2.68	8.71	14.96	0.0073	0.83	17.83	18.40	22.30
12−4	2.59	0.76	2.11	10.23	11.06	0.0039	3.32	7.12	5.50	10.91
3−11	5.16	1.69	3.13	2.26	3.76	0.0005	1.25	9.98	5.42	4.22
1−10	2.50	3.77	1.01	1.93	1.25	0.0001	4.45	5.00	11.79	34.46

The normalization factors are ||e_PM|| = 5.02 rad, ||e_VM|| = 7.05 rad/s and ||e_AM|| = 61.5 rad/s² for position, velocity and acceleration errors, respectively. The errors are evaluated at the via-point (k = v) and at the final point k = T. The expressions pos, vel, and acc identify position, velocity, and acceleration constraints, respectively.